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Uniform superconvergence analysis of Ciarlet‐Raviart scheme for Bi‐wave singular perturbation problem
Author(s) -
Shi Dongyang,
Wu Yanmi
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5254
Subject(s) - superconvergence , mathematics , bilinear interpolation , perturbation (astronomy) , uniqueness , singular perturbation , bilinear form , norm (philosophy) , finite element method , mathematical analysis , law , physics , statistics , quantum mechanics , political science , thermodynamics
Uniform superconvergence analysis of the Ciarlet‐Raviart mixed finite element scheme is discussed for solving the fourth‐order Bi‐wave singular perturbation problem (SPP) by the bilinear element. Firstly, the existence and uniqueness of the approximation solution are proved. Secondly, with the help of the special characters of this element, uniform superclose result of order O ( h 2 ) for the original variable in H 1 norm and uniform optimal order estimate of order O ( h 2 ) for the intermediate variable in L 2 norm are deduced with respect to the real perturbation parameter δ appearing in the considered problem. Furthermore, the global uniform superconvergent estimate is obtained through the interpolated postprocessing approach. Finally, some numerical results are provided to verify the theoretical analysis. Here, h denotes the mesh size.